Answer:
C. 3.6 gallons.
Step-by-step explanation:
Let [tex]X_1[/tex] be the raw score corresponding to z-score 0 and [tex]X_2[/tex] be the raw score corresponding to z-score 3.
We have been given that the number of gallons of gasoline per day used by a car is normally distributed with a mean of 2.2 gallons and a standard deviation of 1.2 gallons.
We will use z-score formula to solve or given problem.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
[tex]z=\text{z-score}[/tex],
[tex]x=\text{Raw-score}[/tex],
[tex]\mu=\text{Mean}[/tex],
[tex]\sigma=\text{Standard deviation}[/tex].
Now we will find raw scores corresponding to given z-scores as:
[tex]0=\frac{X_1-2.2}{1.2}[/tex] and [tex]3=\frac{X_2-2.2}{1.2}[/tex]
Now we will multiply both sides of our equations by 1.2.
[tex]0*1.2=\frac{X_1-2.2}{1.2}*1.2[/tex] and [tex]3*1.2=\frac{X_2-2.2}{1.2}*1.2[/tex]
[tex]0=X_1-2.2[/tex] and [tex]3.6=X_2-2.2[/tex]
Now we will add 2.2 to both sides of our equations.
[tex]0+2.2=X_1-2.2+2.2[/tex] and [tex]3.6+2.2=X_2-2.2+2.2[/tex]
[tex]2.2=X_1[/tex] and [tex]5.8=X_2[/tex]
Now let us find the difference of our both raw scores to find the difference in gallons per day used by both cars.
[tex]\text{Difference in gallons of gasoline used per day}=X_2-X_1[/tex]
[tex]\text{Difference in gallons of gasoline used per day}=5.8-2.2[/tex]
[tex]\text{Difference in gallons of gasoline used per day}=3.6[/tex]
Therefore, the difference in gallons of gasoline used per day by both cars is 3.6 gallons and option C is the correct choice.
